Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 86, pp. 1-9.
Title: Positive solutions and eigenvalues of nonlocal
boundary-value problems
Authors: Jifeng Chu (Hohai Univ., China)
Zhongcheng Zhou (Southwest Normal Univ., China)
Abstract:
We study the ordinary differential equation
$x''+\lambda a(t)f(x)=0$ with the boundary
conditions $x(0)=0$ and $x'(1)=\int_{\eta}^{1}x'(s)dg(s)$.
We characterize values of $\lambda$ for which boundary-value
problem has a positive solution. Also we find appropriate
intervals for $\lambda$ so that there are two positive solutions.
Submitted April 18, 2005. Published July 27, 2005.
Math Subject Classifications: 34B15
Key Words: Nonlocal boundary-value problems;
Positive solutions; eigenvalues;
fixed point theorem in cones.